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a(n) is the smallest number that is the sum of n positive squares in two ways.
10

%I #12 Apr 10 2021 02:48:17

%S 50,27,28,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,

%T 40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,

%U 63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86

%N a(n) is the smallest number that is the sum of n positive squares in two ways.

%C This is r(n,2,2) in Alter's notation.

%H R. Alter, <a href="https://doi.org/10.1007/BFb0096461">Computations and generalizations on a remark of Ramanujan</a>, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981. See Eq. (15), page 188.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = n+15 for n >= 5.

%e a(2) = 50 = 1+49 = 25+25.

%e a(3) = 27 = 1+1+25 = 9+9+9.

%e a(5) = 20 = 1+1+1+1+16 = 4+4+4+4+4.

%Y Cf. A230563, A342902.

%K nonn

%O 2,1

%A _N. J. A. Sloane_, Apr 03 2021